According to Fabrizio Romano, the Blues have offered to loan the player with similar terms to those that Juventus had previously proposed.
The total package being offered is understood to be higher, with Sancho eager to leave Old Trafford for a switch to Stamford Bridge this summer.
Mail Sport previously reported that both clubs were discussing a surprise swap deal involving Sancho and his former England teammate, Raheem Sterling, who was unexpectedly dropped from the Chelsea squad ahead of the Premier League start.
Similarly, the former Borussia Dortmund player was left out of United's games against Fulham and Brighton, and now the winger is keen to revive his career at another club.
The 24-year-old player is understood to be eager to leave Old Trafford after a challenging time in Manchester
Mail Sport previously reported that the clubs held talks over a surprise swap deal involving Sancho and Chelsea outcast Raheem Sterling
The potential move would involve another loan spell for the Red Devils player after he spent the second half of the last season at Signal Iduna Park due to relationship difficulties with manager Erik ten Hag.
According to the Italian football expert, the deal is currently under the jurisdiction of both English clubs, as Juventus put their negotiations on hold on Thursday.
When questioned about the possibility of Sancho's arrival at Stamford Bridge, Chelsea manager Enzo Maresca said: 'If we can sign a player who can help us, for sure I want.
'I know Jadon very well. But he is not our player. We will see what happens.'
It comes after reports that Al-Ahli have hijacked Chelsea's target Ivan Toney, with the player agreeing to move for a transfer fee of £40million
However, Chelsea make late attempts to sign Napoli forward Victor Osimhen, who is also in the Saudi club's shortlist
It is understood that Al-Ahli have made a £55million offer for the striker, prompting Chelsea to bid higher to secure the Nigerian player.